Davenport constant for semigroups. (English) Zbl 1142.20043
Semigroup Forum 76, No. 2, 234-238 (2008); correction ibid. 101, No. 3, 786-794 (2020).
Let \(G\) be a finite commutative semigroup. The Davenport constant \(D(G)\) of \(G\) is the smallest integer \(d\) such that every sequence \(S\) of \(d\) elements in \(G\) contains a subsequence \(T(\neq S)\) with the same product. Let \(R^\times\) be the multiplicative semigroup of the ring \(R=\mathbb{Z}_{n_1}\oplus\cdots\oplus\mathbb{Z}_{n_r}\). The authors show various properties of this semigroup, in particular they determine \(D(R^\times)-D(U(R))\), where \(U(R)\) is the unit group of \(R\).
Reviewer: Robert F. Tichy (Graz)
MSC:
| 20M14 | Commutative semigroups |
| 11B75 | Other combinatorial number theory |
| 20M25 | Semigroup rings, multiplicative semigroups of rings |
Keywords:
finite commutative semigroups; Davenport constants; reducible sequences; homogeneous subsequences; multiplicative semigroups of rings; unit groupsReferences:
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